1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Air resistance problem, expected time.

  1. Aug 1, 2009 #1
    1. The problem statement, all variables and given/known data
    As a bonus question on an assignment for my advanced physics class, we were asked to calculate (approx.) the expected time to impact of a drop of water falling 412m, from a tall building to the ground, considering linear drag. I've done most of the calculations but I expect that I'm missing something in the integrals. It's even more infuriating as they've given a "hint", and I still can't figure it out:

    integral, from 0 to t of (1-e-s/p)ds = t-p(e-t/p)

    which I worked out myself, so I can't quite figure out why they've given me this. Is it just that I can't rearrange this properly to give a value for t, or is there more to it?

    where p is the time constant, p= V/g = 3.374 = m/c where c = 1.55x10-7
    V= terminal velocity = 33.07ms-1
    g= gravitational acceleration= 9.8ms-2
    m= 5.23x10-7
    s= 412m= distance travelled (vertical)

    2. Relevant equations

    with the above, I also have the equations of motion obviously as well as:
    v = -V(1-e-t/p), where v is the velocity at any given point (intially 0)

    3. The attempt at a solution

    So far all I've worked out is the terminal velocity and time constant (given above)
    I think I need to use the height s (412m) and some relation between the time constant, terminal velocity and time but can't work through the maths.

    Thanks heaps
     
  2. jcsd
  3. Aug 1, 2009 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi emmaeng! Welcome to PF! :smile:

    I'm not sure why it's not working out for you, but it may be because this equation is wrong …
    if you put t = 0, you don't get 0, do you? :wink:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Air resistance problem, expected time.
Loading...